Download or read book Graphs Colourings and the Four Colour Theorem written by Robert A. Wilson and published by OUP Oxford. This book was released on 2002-01-24 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: The four-colour theorem is one of the famous problems of mathematics, that frustrated generations of mathematicians from its birth in 1852 to its solution (using substantial assistance from electronic computers) in 1976. The theorem asks whether four colours are sufficient to colour all conceivable maps, in such a way that countries with a common border are coloured with different colours. The book discusses various attempts to solve this problem, and some of the mathematics which developed out of these attempts. Much of this mathematics has developed a life of its own, and forms a fascinating part of the subject now known as graph theory. The book is designed to be self-contained, and develops all the graph-theoretical tools needed as it goes along. It includes all the elementary graph theory that should be included in an introduction to the subject, before concentrating on specific topics relevant to the four-colour problem. Part I covers basic graph theory, Euler's polyhedral formula, and the first published false `proof' of the four-colour theorem. Part II ranges widely through related topics, including map-colouring on surfaces with holes, the famous theorems of Kuratowski, Vizing, and Brooks, the conjectures of Hadwiger and Hajos, and much more besides. In Part III we return to the four-colour theorem, and study in detail the methods which finally cracked the problem.
Download or read book The Four Color Theorem written by Rudolf Fritsch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses a famous problem that helped to define the field now known as topology: What is the minimum number of colors required to print a map so that no two adjoining countries have the same color? This problem remained unsolved until the 1950s, when it was finally cracked using a computer. This book discusses the history and mathematics of the problem, as well as the philosophical debate which ensued, regarding the validity of computer generated proofs.
Download or read book Four Colors Suffice written by Robin J. Wilson and published by Princeton University Press. This book was released on 2002 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: On October 23, 1852, Professor Augustus De Morgan wrote a letter to a colleague, unaware that he was launching one of the most famous mathematical conundrums in history--one that would confound thousands of puzzlers for more than a century. This is the amazing story of how the "map problem" was solved. The problem posed in the letter came from a former student: What is the least possible number of colors needed to fill in any map (real or invented) so that neighboring counties are always colored differently? This deceptively simple question was of minimal interest to cartographers, who saw little need to limit how many colors they used. But the problem set off a frenzy among professional mathematicians and amateur problem solvers, among them Lewis Carroll, an astronomer, a botanist, an obsessive golfer, the Bishop of London, a man who set his watch only once a year, a California traffic cop, and a bridegroom who spent his honeymoon coloring maps. In their pursuit of the solution, mathematicians painted maps on doughnuts and horseshoes and played with patterned soccer balls and the great rhombicuboctahedron. It would be more than one hundred years (and countless colored maps) later before the result was finally established. Even then, difficult questions remained, and the intricate solution--which involved no fewer than 1,200 hours of computer time--was greeted with as much dismay as enthusiasm. Providing a clear and elegant explanation of the problem and the proof, Robin Wilson tells how a seemingly innocuous question baffled great minds and stimulated exciting mathematics with far-flung applications. This is the entertaining story of those who failed to prove, and those who ultimately did prove, that four colors do indeed suffice to color any map.
Download or read book The Four color Problem written by Thomas L. Saaty and published by . This book was released on 1986 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Four Color Problem written by and published by Academic Press. This book was released on 2011-08-29 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Four-Color Problem
Download or read book Every Planar Map is Four Colorable written by Kenneth I. Appel and published by American Mathematical Soc.. This book was released on 1989 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume, the authors present their 1972 proof of the celebrated Four Color Theorem in a detailed but self-contained exposition accessible to a general mathematical audience. An emended version of the authors' proof of the theorem, the book contains the full text of the supplements and checklists, which originally appeared on microfiche. The thiry-page introduction, intended for nonspecialists, provides some historical background of the theorem and details of the authors' proof. In addition, the authors have added an appendix which treats in much greater detail the argument for situations in which reducible configurations are immersed rather than embedded in triangulations. This result leads to a proof that four coloring can be accomplished in polynomial time.
Download or read book The Four color Problem written by Thomas L. Saaty and published by . This book was released on 1977 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Graphs Colourings and the Four colour Theorem written by and published by . This book was released on 2002 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robert Wilson discusses the four-colour theorem and some of the mathematics which developed out of attempts to solve it. He covers basic graph theory, Euler's polyhedral formula and the first published false solution of the four-colour problem.
Download or read book Graph Edge Coloring written by Michael Stiebitz and published by John Wiley & Sons. This book was released on 2012-02-27 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features recent advances and new applications in graph edgecoloring Reviewing recent advances in the Edge Coloring Problem, GraphEdge Coloring: Vizing's Theorem and Goldberg's Conjectureprovides an overview of the current state of the science,explaining the interconnections among the results obtained fromimportant graph theory studies. The authors introduce many newimproved proofs of known results to identify and point to possiblesolutions for open problems in edge coloring. The book begins with an introduction to graph theory and theconcept of edge coloring. Subsequent chapters explore importanttopics such as: Use of Tashkinov trees to obtain an asymptotic positive solutionto Goldberg's conjecture Application of Vizing fans to obtain both known and newresults Kierstead paths as an alternative to Vizing fans Classification problem of simple graphs Generalized edge coloring in which a color may appear more thanonce at a vertex This book also features first-time English translations of twogroundbreaking papers written by Vadim Vizing on an estimate of thechromatic class of a p-graph and the critical graphs within a givenchromatic class. Written by leading experts who have reinvigorated research inthe field, Graph Edge Coloring is an excellent book formathematics, optimization, and computer science courses at thegraduate level. The book also serves as a valuable reference forresearchers interested in discrete mathematics, graph theory,operations research, theoretical computer science, andcombinatorial optimization.
Download or read book Chromatic Graph Theory written by Gary Chartrand and published by CRC Press. This book was released on 2019-11-28 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: With Chromatic Graph Theory, Second Edition, the authors present various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. Readers will see that the authors accomplished the primary goal of this textbook, which is to introduce graph theory with a coloring theme and to look at graph colorings in various ways. The textbook also covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings. Features of the Second Edition: The book can be used for a first course in graph theory as well as a graduate course The primary topic in the book is graph coloring The book begins with an introduction to graph theory so assumes no previous course The authors are the most widely-published team on graph theory Many new examples and exercises enhance the new edition
Download or read book Graph Coloring Problems written by Tommy R. Jensen and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a wealth of information previously scattered in research journals, conference proceedings and technical reports. Identifies more than 200 unsolved problems. Every problem is stated in a self-contained, extremely accessible format, followed by comments on its history, related results and literature. The book will stimulate research and help avoid efforts on solving already settled problems. Each chapter concludes with a comprehensive list of references which will lead readers to original sources, important contributions and other surveys.
Download or read book A Guide to Graph Colouring written by R.M.R. Lewis and published by Springer. This book was released on 2015-10-26 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats graph colouring as an algorithmic problem, with a strong emphasis on practical applications. The author describes and analyses some of the best-known algorithms for colouring arbitrary graphs, focusing on whether these heuristics can provide optimal solutions in some cases; how they perform on graphs where the chromatic number is unknown; and whether they can produce better solutions than other algorithms for certain types of graphs, and why. The introductory chapters explain graph colouring, and bounds and constructive algorithms. The author then shows how advanced, modern techniques can be applied to classic real-world operational research problems such as seating plans, sports scheduling, and university timetabling. He includes many examples, suggestions for further reading, and historical notes, and the book is supplemented by a website with an online suite of downloadable code. The book will be of value to researchers, graduate students, and practitioners in the areas of operations research, theoretical computer science, optimization, and computational intelligence. The reader should have elementary knowledge of sets, matrices, and enumerative combinatorics.
Download or read book Handbook of Combinatorial Optimization written by Ding-Zhu Du and published by Springer Science & Business Media. This book was released on 2006-08-18 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a supplementary volume to the major three-volume Handbook of Combinatorial Optimization set. It can also be regarded as a stand-alone volume presenting chapters dealing with various aspects of the subject in a self-contained way.
Download or read book Fuzzy Graph Theory written by Sunil Mathew and published by Springer. This book was released on 2017-12-30 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a timely overview of fuzzy graph theory, laying the foundation for future applications in a broad range of areas. It introduces readers to fundamental theories, such as Craine’s work on fuzzy interval graphs, fuzzy analogs of Marczewski’s theorem, and the Gilmore and Hoffman characterization. It also introduces them to the Fulkerson and Gross characterization and Menger’s theorem, the applications of which will be discussed in a forthcoming book by the same authors. This book also discusses in detail important concepts such as connectivity, distance and saturation in fuzzy graphs. Thanks to the good balance between the basics of fuzzy graph theory and new findings obtained by the authors, the book offers an excellent reference guide for advanced undergraduate and graduate students in mathematics, engineering and computer science, and an inspiring read for all researchers interested in new developments in fuzzy logic and applied mathematics.
Download or read book Introduction to Graph Theory written by Koh Khee Meng and published by World Scientific Publishing Company. This book was released on 2007-03-15 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college. The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.
Download or read book Discrete Mathematics written by Oscar Levin and published by Createspace Independent Publishing Platform. This book was released on 2018-07-30 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Note: This is a custom edition of Levin's full Discrete Mathematics text, arranged specifically for use in a discrete math course for future elementary and middle school teachers. (It is NOT a new and updated edition of the main text.)This gentle introduction to discrete mathematics is written for first and second year math majors, especially those who intend to teach. The text began as a set of lecture notes for the discrete mathematics course at the University of Northern Colorado. This course serves both as an introduction to topics in discrete math and as the "introduction to proof" course for math majors. The course is usually taught with a large amount of student inquiry, and this text is written to help facilitate this.Four main topics are covered: counting, sequences, logic, and graph theory. Along the way proofs are introduced, including proofs by contradiction, proofs by induction, and combinatorial proofs.While there are many fine discrete math textbooks available, this text has the following advantages: - It is written to be used in an inquiry rich course.- It is written to be used in a course for future math teachers.- It is open source, with low cost print editions and free electronic editions.
Download or read book History of Topology written by I.M. James and published by Elsevier. This book was released on 1999-08-24 with total page 1067 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.
